Pietro Freni (Leeds)
- Date
- Wednesday 14 February 2024, 2.00 PM
- Location
- MALL
- Category
- Models Seminar
Weakly immediate types and T-convexity
For $T$ an o-minimal theory expanding RCF, a $T$-convex valuation ring on an o-minimal expansion of a RCF is a convex subring closed under continuous $T$-definable functions. This was first defined by Van Den Dries and Leweneberg who proved that the common theory $T_{\mathrm{convex}}$ of the expansions of models of $T$ by a non-trivial $T$-convex valuation ring is complete and weakly o-minimal. One of the key properties of the valuation theory of $T_{\mathrm{convex}}$ for power bounded $T$ is the so called residue-valuation property which can be restated as saying that every model of $T_{\mathrm{convex}}$ has a spherically complete maximal immediate extension. This is known to be false if $T$ defines an exponential. The goal of the talk will be to discuss potential analogues of the residue-valuation property in the exponential context.